About The Writer
Mr Jason Hu
With a decade of experience teaching IBDP Math (AA/AI HL and SL) and 7 years as an examiner, Mr Hu is deeply involved in shaping student success. He’s been part of IA moderation for May 2020-2022 and marked AAHL Paper 2 for May 2023-2024. Currently, he brings his expertise to leading international schools across China and Singapore, helping students thrive in the IBDP journey.
The essence of Paper 3 lies in consolidating various knowledge points into comprehensive, exploratory questions.
First and foremost, it’s important to note that no teacher can predict what questions will appear on the next IB exam’s Paper 3. Unlike Papers 1 and 2, which follow a set format and structure, Paper 3 is unique in its approach. The essence of Paper 3 lies in consolidating various knowledge points into comprehensive, exploratory questions. This exploration typically involves a specific mathematical concept, and sometimes even one that is not explicitly covered in the syllabus.
Students are required to utilize their foundational knowledge to arrive at interesting, yet challenging, conclusions. Some students could be overwhelmed by the unfamiliar settings of the questions and panic during the exam. However, the motivation of the paper is to let the students explore a new entire Mathematics concept using only what they have learned in the syllabus.
Here is a breakdown of how IBDP grades are calculated in Math HL (both Analysis & Approaches and Application & Interpretation):
From the table above, we can see:
- The score for IA is the most valuable—each point contributes 1 percent to the final grade.
- Among the three papers, Paper 3 holds the most value—although its total score is only half that of Papers 1 and 2, it accounts for 20% of the final calculation (equivalent to 2/3 of the combined total of Paper 1 and Paper 2).
Typical Paper 3 questions are usually around 25 to 30 marks each, and they can encompass a wide array of topics. As a student, it’s crucial to pay attention to the Additional Higher Level (AHL) content specified in the syllabus. The most frequently tested topics include complex numbers, differential calculus, functions and graphs, number patterns, and proof techniques. Interestingly, there are very few questions on vectors in Paper 3. This is likely because vector questions typically appear in Paper 1, which does not allow the use of a Graphing Display Calculator (GDC). Therefore, vectors are not often included in Paper 3.
Given the unpredictable nature of Paper 3, we shouldn’t attempt to guess which topics will appear in future exams or the specific types of questions that may be asked. Instead, we should focus our efforts on the knowledge points and problem-solving techniques that are commonly assessed in these questions. Developing a solid understanding of these concepts will better prepare you for whatever challenges may arise. In essence, anything can be tested so students are advised to sharpen their foundations.
Given the unpredictable nature of Paper 3 (…) we should focus our efforts on the knowledge points and problem-solving techniques that are commonly assessed in these questions.
6 Practical Tips to Boost Your Paper 3 Score
To achieve a high score, especially if you feel your skills are not yet strong, it is essential to strengthen a few key areas:
1.
The questions are arranged by the examiner on purpose.
The test questions are intentionally arranged to guide your knowledge process, with the examiner introducing a new concept through the test.
The initial questions serve as foundational, easy-to-understand problems that help you grasp the basics. As you progress, the questions become more challenging, requiring logic jumps, applications, and inferences that build on what you’ve just learned. Utilize new knowledge found from the earlier parts to build new knowledge.
Finally, the test concludes with one or two questions designed to assess your overall understanding of the concept, which you develop through all the other question parts.
This deliberate order ensures you acquire the necessary knowledge and realizations before tackling the final questions.
2.
Ensure you get the basic questions right; aim for full marks on simple points.
All Paper 3 questions typically start from very simple base cases, often providing some easier questions at the outset. It is crucial to secure full marks on these foundational questions. Not only do they contribute valuable points to your overall score, but they also help build your confidence, enabling you to tackle the more complex questions that follow with a clearer mindset.
Remember, a strong start can set the tone for the rest of your performance.
3.
Be mindful of how many points are allocated for each part of the question.
Pay careful attention to the marking scheme. You should avoid spending excessive time on any 1 or 2 mark question, especially if it requires a lengthy solution. If you are finding yourself devoting much time and effort to what appears to be a simple problem, it may indicate that you are on the wrong track. Conversely, if you are providing only a few steps for a question that is worth significantly more marks, it is important to reassess your approach. Ensure you haven’t overlooked any crucial points or additional cases that should be considered in your solution.
Pay attention to the command terms. If you are asked to ‘show or explain’ usually you are supposed to give strong deductions and proofs. If you are asked to ‘write down’ some result, usually the steps are not required (especially when there’s only one mark to the question).
Being strategic about how you allocate your time can greatly enhance your overall performance.
4.
Learn to utilize existing answers and conclusions.
Here is a real Paper 3 question from May 2022.
You should note that in question (e), which asks you to find the smallest triangular and pentagonal positive integers, what you need to do is immediately refer back to the properties of triangular and pentagonal numbers discussed in questions (c) and (d). Create a table or use a calculator to identify the smallest positive integer that satisfies both properties.
By using previously discussed properties or solutions, you can streamline your problem-solving process.
5.
Proof Techniques Must Be Strengthened
There is a strong emphasis on proof problems in the AA course. The following questions are from recent past papers, and you’ll notice that almost all Paper 3 exams include a high-scoring question that requires proof by induction, here are some examples:
2023 May Paper 3
2022 Nov Paper 3
(Of course, aside from induction, other types of proofs will also be tested. One area that our students usually struggle with is proof by contradiction.)
When learning the method of induction, make sure not to limit your practice to just simple sequences or basic divisibility problems and think you have mastered it. Try to apply induction in various settings such as in calculus (higher derivative results), functions (properties of composite functions etc).
There is a strong emphasis on proof problems in the AA course.
6.
The Use of GDC is Very Important
Similar to Paper 2, for any question, as long as you can use the GDC to obtain a result—even if the process is incomplete—you can earn points (not necessarily full marks, but you can score most of the points).
For Paper 3, some specific GDC usage scenarios include:
- Listing numbers to find patterns
- Using graphs to find solutions to complicated equations or function values
- Finding the first, second, or even higher derivatives of any function
- Finding the stationary values of a function, from a graph. Sometimes you may be required to state/use the nature of such stationary points.
Students who are not proficient with the GDC must practice the relevant problem-solving techniques. I often see some students relying on scientific calculators as a substitute, which can lead to many issues during the exam.
I often see some students relying on scientific calculators as a substitute, which can lead to many issues during the exam.
I hope these insights provide valuable guidance for all HL students as they prepare for Paper 3. By focusing on the key areas mentioned, you can approach this challenging exam with confidence. Remember, consistent practice and strategic preparation are essential to success. Good luck on your journey toward achieving your best in IBDP Math HL.
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